2. (10 points) Let X and Y be continuous random variables with correlation coefficient given by PXY = 1. When the mean a

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2 10 Points Let X And Y Be Continuous Random Variables With Correlation Coefficient Given By Pxy 1 When The Mean A 1 (50.42 KiB) Viewed 28 times

Let X and Y be continuous random variables with correlation
coefficient given by ρ_XY=1.
When the mean and standard deviation of X are denoted by μ_X and
σ_X>0,repectively,
and the mean and standard devication of Y are denoted by μ_Y and
σ_Y>0,answer the following questions.
(a) What is the definition of ρ_XY in terms of μ_X, σ_X, μ_Y and
σ_Y?
(b) Given the event {Y=y}, find conditional pdf of X.
2. (10 points) Let X and Y be continuous random variables with correlation coefficient given by PXY = 1. When the mean and standard deviation of X are denoted by px and ox > 0, respectively, and the mean and standard deviation of Y are denoted uy and oy > 0, answer the following questions. (a) (5 points) What is the definition of pxy in terms of x, ox,fly, and oy? (b) (5 points) Given the event {Y = y}, find conditional pdf of X.